A difference is that qu'est-ce à dire, like other interrogatives using an inversion, is less mainstream and more formal. On the opposite, you might hear qu'est-ce ça veut dire ? (dropping que), ça veut dire quoi / tu veux dire quoi ? in colloquial spoken French.

There might also be a slight nuance. Qu'est-ce que ça veut dire ? often simply means that the wording of what has been said is not understood while qu'est-ce à dire ? might mean that while the words are understood, the underlying meaning need to be clarified like with qu'est-ce que tu veux dire par là / qu'est-ce qui est sous entendu par là ?

The two are different words, they cannot be used in the same context to mean the same thing. "That is" can be used to mean for example/instance. While 'What does this mean?' is used for asking a question.

The fact that the two represent two different wordings is obviously very true. However, this is in no way a sufficient reason for their meanings to necessarily differ. In this precise case, they do actually not necessarily differ.
– aCOSwtOct 7 '18 at 22:33